Let's take his argument in the quote true as given (I don't know the relevant neuroscience here either). So we'll assume that all non-human animals only have level 1 or 2 awareness of pain. Now you need to figure out which sort of pain it is that you value preventing - level 1, 2, or 3 (presumably if you value preventing 1, you value preventing 2 and 3 as well). If you only value preventing level 3 pain, then eat away. If level 2, then don't eat vertebrates. If level 1, don't eat any organism that reacts to negative stimuli (all organisms?). This is ultimately a values question.
Note that if preventing animals from feeling some sort of pain is the only reason you're a vegetarian, then consider whether you would eat animals who were killed in a non-pain inducing way (in any/all of the three senses). If you don't think eating the animals is ok in that situation, then think about what your true rejection of eating animals is.
I would eat animals if they were killed in a non-pain inducing way, in so far as they don't have the same kind of interests in "continuing to live" as (nearly all) humans do. Unfortunately, animals are most definitely not kept or killed in non-pain inducing ways.
I ended up reading this article about animal suffering by this Christian apologist called William Craig. Forgive the source, please.
He continues the argument here.
How decent do you think this argument is? I don't know where to look to evaluate the core claim, as I know very little neuroscience myself. I'm quite concerned about animal suffering, and choose to be vegetarian largely on the basis of that concern. How much should my decision on that be affected by this argument?
EDIT: David_Gerard wins by doing the basic Google search that I neglected. It seems that the argument is flawed. Particularly, animals apart from primates have pre-frontal cortexes.